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SEO Keyword summary for en.wikipedia.org/wiki/angular_momentum_operator
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
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Short Tail Keywords displaystyle angular momentum |
long Tail Keywords (2 words) angular momentum commutation relations orbital angular quantum mechanics partial partial |
long Tail Keywords (3 words) orbital angular momentum total angular momentum frac partial partial angular momentum operator partial partial phi angular momentum operators spin angular momentum |
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angular momentum operator wikipedia
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wikipedia free encyclopedia displaystyle ihbar frac ddtpsi rangle hat hpsi mathbf times leftlxlylzright nabla leftsxsyszright leftjxjyjzright leftlxlyrightihbar lzleftlylzrightihbar lxleftlzlxrightihbar xyequiv xyyx leftlllmrightihbar sum varepsilon lmnln xlpmihbar delta leftliljrightvarepsilon ijklk leftslsmrightihbar lmnsnquad leftjljmrightihbar lmnjn operatorname equiv leftl lxrightleftl lyrightleftl lzright beginalignedleftl lxrightleftlx lxrightleftly lxrightleftlz lxrightlyleftlylxrightleftlylxrightlylzleftlzlxrightleftlzlxrightlzlyleftihbar lzrightleftihbar lzrightlylzleftihbar lyrightleftihbar lyrightlz endaligned beginalignedlefts siright leftj jiright sigma lxsigma lygeq hbar leftlangle lzrangle right langle xrangle lxlylz ell ldots mell lxorly tfrac msss sxorsy mjjj jxorjy beginalignedjequiv jxijyjequiv jxijyendaligned psi jpsi jzj textstyle jzleq sqrt jyjzihbar jxjzjxihbar jzjxpm ijyjxpm ijyjzpm beginalignedjzjxpm ijypsi jzjzpm jxpm jzendaligned jzpm ijy leq jxijypsi jxijy jjjx ijxjyjx geq dots jhbar jzjhbar beginalignedjzmjhbar lzihbar partial phi lzpsi aeilzphi beginalignedaeilzphi eilz lzmlhbar lefttfrac rightrangle eiphi sin theta lzqxpyqypx beginalignedq qxpysqrt pxqysqrt lztfrac leftp righttfrac beginalignedh righth rightendaligned beginalignedl mpsi leftn rightpsi mleftn rightleftn rightn lsqrt lzhbar rhat nphi rightarrow jhat nequiv lim rlefthat leftihbar rightpartial rightphi rightrlefthat rightexp leftfrac iphi nhbar rtextspatiallefthat lhat rtextinternallefthat shat rightrtextinternallefthat rightrtextspatiallefthat circ rtextspatial rtextinternal left ilzhbar mhbar rightleftpsi mathfrak rhr hmathbf leftmathbf rightzleftj jin leftleftj rightleftleftj rightldots rightright beginalignedmathbf boldsymbol sintheta rightihbar lefthat leftsinphi cottheta cosphi righthat leftcosphi sinphi rightlhbar icottheta rightl leftsintheta rightfrac rightlzihbar rleftr rrightfrac leftell mrightrangle lzleftell mleftell yell mtheta gamma wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/angular_momentum_operator
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angular found in path !
momentum found in path !
operator found in path !
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w httpsenwikipediaorgwindexphptitleangularmomentumoperatoroldid1245589983
page information
printable version
quantum correlator
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wiki quantum mechanics
schrdinger
introduction
history
classical mechanics
old quantum theory
braket notation
hamiltonian
interference
complementary observables
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spinuniqtemplatestyles00000056qinu12 particle
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identity operator
matrix exponential
stones theorem on oneparameter unitary groups
lie groups
particle physics and representation theory
representation theory of su2
rotation group so3 a note on lie algebras
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representation
ehrenfest theorem
central potential
angular momentum coupling
spinorbit coupling
bases
term symbol
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laplace operator
eigenstates of the operator
spherical harmonics
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jordan map
schwinger
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angular momentum diagrams quantum mechanics
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tensor operator
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richard l liboff
isbn
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issn
littlejohn robert
prentice hall
condon e u
arxiv
s2cid
classical l
modern quantum mechanics
biedenharn l c
dalembertian
parity
time
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bfc53d0ffe7111f9255d9562b522f2983b932db8 height: height attribute not set width: width attribute not set description: {\displaystyle s=0,{\tfrac {1}{2}},1,{\tfrac {3}{2}},\ldots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bf685f2b7d1c4266b32c1e16fdc6a41a610ab21e height: height attribute not set width: width attribute not set description: {\displaystyle s_{z}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dbf0a102d8fc7b1b9813dcf8fa8cd9d931ffa4a7 height: height attribute not set width: width attribute not set description: {\displaystyle \hbar m_{s}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7d7b42065bbfd0e946e56a3f37e9364bd5587996 height: height attribute not set width: width attribute not set description: {\displaystyle m_{s}=-s,(-s+1),\ldots ,(s-1),s} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/488560816fccdf62695552ac8bf0611a0d5c09b4 height: height attribute not set width: width attribute not set description: {\displaystyle m_{s}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ac8a515de34f0af7d15de46f73bf674950d444a8 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {s} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0c8adac3506f5b69d14662c683cc705e750ecf86 height: height attribute not set width: width attribute not set description: {\displaystyle s_{x}\,or\,s_{y}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6fa18f680f853f4b3462401d4012c9b430b88b4f height: height attribute not set width: width attribute not set description: {\displaystyle j^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fc58b7fc4bcbf6398448d419a219cb7488caf7d0 height: height attribute not set width: width attribute not set description: {\displaystyle \hbar ^{2}j(j+1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ffdb7c0046e9a90fd1f01f7ca09f5335bc0fd32b height: height attribute not set width: width attribute not set description: {\displaystyle j=0,{\tfrac {1}{2}},1,{\tfrac {3}{2}},\ldots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5e4fc97aafeb0dc8febc33638f7644e68c2f68ac height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b2cbbd8455e82b2da88947f01248f416ab6ab5d1 height: height attribute not set width: width attribute not set description: {\displaystyle \hbar m_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f37c471107e137216c65eeb28cc87da06fad7fb3 height: height attribute not set width: width attribute not set description: {\displaystyle m_{j}=-j,(-j+1),\ldots ,(j-1),j} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/14f2b12b1676ba2f42ad8d2c9ee6aa46e7667b73 height: height attribute not set width: width attribute not set description: {\displaystyle m_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7686846b1a6b756cb514954000004ab5e7b2a5ba height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {j} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d38fd2c40b6c75053e69e04fa2c7d21877954d3b height: height attribute not set width: width attribute not set description: {\displaystyle j_{x}\,or\,j_{y}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c0c992d4fe07df26d2e8e67adb6e23966f40b6dc height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}j_{+}&\equiv j_{x}+ij_{y},\\j_{-}&\equiv j_{x}-ij_{y}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cc27f1893b769a08cd6b296e115a29e61cab675e height: height attribute not set width: width attribute not set description: {\displaystyle |\psi \rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2e563bf0b455248b931727624197d639271f1cc5 height: height attribute not set width: width attribute not set description: {\displaystyle j_{+}|\psi \rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1446915bcbaaa32eb0fd6930acffd1cda18e04f1 height: height attribute not set width: width attribute not set description: {\displaystyle j_{-}|\psi \rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d6f24269158ec55f392c5076c52a6a131cc1e871 height: height attribute not set width: width attribute not set description: {\displaystyle \psi ({j^{2}}'j_{z}')} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/970cecab23804ff86ce29e70f69d6ba3096bd5cc height: height attribute not set width: width attribute not set description: {\displaystyle {j^{2}}'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0bf5e9f66d9015550472bd36494c953022982b99 height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7c1335a7eaecf80587621548a6d7f8fe69593acc height: height attribute not set width: width attribute not set description: {\displaystyle j^{2}=j_{x}^{2}+j_{y}^{2}+j_{z}^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4375edabf03becd56b6cee32025719ee4d9df54b height: height attribute not set width: width attribute not set description: {\displaystyle j_{x}^{2}+j_{y}^{2}=j^{2}-j_{z}^{2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/71aac54ad945d847923386dfbdb28612f6e03771 height: height attribute not set width: width attribute not set description: {\displaystyle (j_{x}^{2}+j_{y}^{2})\;\psi ({j^{2}}'j_{z}')=({j^{2}}'-j_{z}'^{2})\;\psi ({j^{2}}'j_{z}').} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/573c4eac7701ac45330a1677abe1c3a7fc054ae1 height: height attribute not set width: width attribute not set description: {\displaystyle j_{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/782c237016b7230689619e010bf692a0adc79b38 height: height attribute not set width: width attribute not set description: {\displaystyle j_{y}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d3b59b797f9b0c709cbb3fc85d1506b2dfaae4c9 height: height attribute not set width: width attribute not set description: {\displaystyle {j^{2}}'-j_{z}'^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9021e0076efe663845146ec488564eb10cdf8503 height: height attribute not set width: width attribute not set description: {\textstyle |j_{z}'|\leq {\sqrt {{j^{2}}'}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7eeb3ba71de968e573852eb052632b0e3b111eb0 height: height attribute not set width: width attribute not set description: {\displaystyle [j_{y},j_{z}]=i\hbar j_{x},\;\;[j_{z},j_{x}]=i\hbar j_{y}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/869e366caf596564de4de06cb0ba124056d4064b height: height attribute not set width: width attribute not set description: {\displaystyle \pm } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e73de4c9121d04a2eb77fe5290207ed31b56b859 height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}(j_{x}\pm ij_{y})=(j_{x}\pm ij_{y})(j_{z}\pm \hbar ),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406 height: height attribute not set width: width attribute not set description: {\displaystyle +} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/04bd52ce670743d3b61bec928a7ec9f47309eb36 height: height attribute not set width: width attribute not set description: {\displaystyle -} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/01b55337e991e1f399cdd1a4eee5c2d277326759 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}j_{z}(j_{x}\pm ij_{y})\;\psi ({j^{2}}'j_{z}')&=(j_{x}\pm ij_{y})(j_{z}\pm \hbar )\;\psi ({j^{2}}'j_{z}')\\&=(j_{z}'\pm \hbar )(j_{x}\pm ij_{y})\;\psi ({j^{2}}'j_{z}')\;.\\\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f0f7ff72de2f0ca9f7fcb12c7d54ef1d8fa688b6 height: height attribute not set width: width attribute not set description: {\displaystyle (j_{x}\pm ij_{y})\;\psi ({j^{2}}'j_{z}')} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/67996f813df430d6ae9db961cd707828d21bd3bb height: height attribute not set width: width attribute not set description: {\displaystyle {j_{z}}'\pm \hbar } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c5a13c0e4608caf25f90e5d808d1d18b7648a6f2 height: height attribute not set width: width attribute not set description: {\displaystyle \psi ({j^{2}}'j_{z}'\pm \hbar )=(j_{x}\pm ij_{y})\;\psi ({j^{2}}'j_{z}').} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4041fec2b1e191db5cce2b6bdf8ec2945764655c height: height attribute not set width: width attribute not set description: {\displaystyle j_{x}\pm ij_{y}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d073cd0c5e7ea9ac3bb8221d56768f6d64aa2698 height: height attribute not set width: width attribute not set description: {\displaystyle \leq {\sqrt {{j^{2}}'}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/01a8ecd3ccd7cfe376f13f8072b0569c2b86fe2c height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5a2a06f114cb93bfeb44629445e8dfbeee58df5f height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/490d9a9d0f4658959c1bb14b11dddb4bbe238235 height: height attribute not set width: width attribute not set description: {\displaystyle (j_{x}-ij_{y})\;\psi ({j^{2}}'j_{z}^{0})=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af0a6f891ac076477431a599f15a355158697dca height: height attribute not set width: width attribute not set description: {\displaystyle (j_{x}+ij_{y})\;\psi ({j^{2}}'j_{z}^{1})=0,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e71c81f1b902dabf865de8de6a2f476efe1c2e30 height: height attribute not set width: width attribute not set description: {\displaystyle |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0fbdf0e8ae9038d4a3d75c3de0efc993bbe5425a height: height attribute not set width: width attribute not set description: {\displaystyle >j_{z}^{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dc09dcefcaab6fc939c87968210ef342dff93c10 height: height attribute not set width: width attribute not set description: {\displaystyle (j_{x}+ij_{y})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ba90e2d3fe7c6a442a7023fbd61927456eb73795 height: height attribute not set width: width attribute not set description: {\displaystyle (j_{x}-ij_{y})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/012854292a94610e4b704dc29af631ac6fd10323 height: height attribute not set width: width attribute not set description: {\displaystyle j_{x}^{2}+j_{y}^{2}=j^{2}-j_{z}^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a70ccf94f0585ff6e71f735d8053e39aaf4ccae6 height: height attribute not set width: width attribute not set description: {\displaystyle j_{+}j_{-}=j_{x}^{2}+j_{y}^{2}-i[j_{x},j_{y}]=j_{x}^{2}+j_{y}^{2}+j_{z}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d445875534c7ba0e5cbcec3bfe47691c82eeff01 height: height attribute not set width: width attribute not set description: {\displaystyle {j^{2}}'-(j_{z}^{0})^{2}+\hbar j_{z}^{0}=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d034170c2b27b45025f57191d0ce01eec69c7969 height: height attribute not set width: width attribute not set description: {\displaystyle {j^{2}}'-(j_{z}^{1})^{2}-\hbar j_{z}^{1}=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/428f3b86879413aae1ce8ca54b427904d3ae2185 height: height attribute not set width: width attribute not set description: {\displaystyle (j_{z}^{1}+j_{z}^{0})(j_{z}^{0}-j_{z}^{1}-\hbar )=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f8c75ba1b74c0bff0c4bb83d837dedc386f61c7 height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{1}\geq j_{z}^{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/61068fd1ac6cc7459d2f69ac8882253393af4136 height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{0}=-j_{z}^{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/48ef03c81513f17be7c22a0e3de7550e00d385dc height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{1}-j_{z}^{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d8772b88585697dd5e979157a4be86de283f8e3 height: height attribute not set width: width attribute not set description: {\displaystyle j_{x}-ij_{y}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a6147225789f107b54eb1b02cb5a1b643a745690 height: height attribute not set width: width attribute not set description: {\displaystyle j_{x}+ij_{y}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a129e4c7ae2a5833777c0ab4c26d82b5ddbbb978 height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{1}-j_{z}^{0}=0,\hbar ,2\hbar ,\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8675bf0a49e8b115fe90677f5438009eb7a65d71 height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{1}-j_{z}^{0}=2j\hbar ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6ad42fc01db6e61db3f988cb42dc07a3368c43be height: height attribute not set width: width attribute not set description: {\displaystyle j=0,{\tfrac {1}{2}},1,{\tfrac {3}{2}},\dots \;.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a3e42cfa74ff34282fd40e273d1a64fb140eb567 height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{0}=-j\hbar } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3c181a8b69508be361afe78f05955a21a8909aa height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}^{1}=j\hbar ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2129e172e0377113c90637e462dc164dfb45f4e9 height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}'=-j\hbar ,-j\hbar +\hbar ,-j\hbar +2\hbar ,\dots ,j\hbar .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1c46c03f669805b86282a756b5a7f3cfa5a0a177 height: height attribute not set width: width attribute not set description: {\displaystyle m_{j}\;} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e6378e4c9fcd13a5692de37a573ca4105101fe1c height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}j_{z}'&=m_{j}\hbar &m_{j}&=-j,-j+1,-j+2,\dots ,j\\{j^{2}}'&=j(j+1)\hbar ^{2}&j&=0,{\tfrac {1}{2}},1,{\tfrac {3}{2}},\dots \;.\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/950c18c5e2ebbfec60d60944c2581d8a7604b55d height: height attribute not set width: width attribute not set description: {\displaystyle l_{z}=-i\hbar {\frac {\partial }{\partial \phi }}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a height: height attribute not set width: width attribute not set description: {\displaystyle \psi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3a91ae3d63ef2538f91cbe22046526991b3ddb3a height: height attribute not set width: width attribute not set description: {\displaystyle l_{z}'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/66b39ad0e97437f10b6fbec7a76d1d003a126b64 height: height attribute not set width: width attribute not set description: {\displaystyle -i\hbar {\frac {\partial }{\partial \phi }}\psi =l_{z}'\psi .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5917d8d265967c9509054b1e662db839276e7916 height: height attribute not set width: width attribute not set description: {\displaystyle \psi =ae^{il_{z}'\phi /\hbar },} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3 height: height attribute not set width: width attribute not set description: {\displaystyle a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4 height: height attribute not set width: width attribute not set description: {\displaystyle \phi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/73efd1f6493490b058097060a572606d2c550a06 height: height attribute not set width: width attribute not set description: {\displaystyle 2\pi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/974e6f920d9f0677551d0980c3f8b6c73c244fe8 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}ae^{il_{z}'(\phi +2\pi )/\hbar }&=ae^{il_{z}'\phi /\hbar },\\e^{il_{z}'2\pi /\hbar }&=1.\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ce1af4edbd84f8b2db9c72090dc1863ba5220145 height: height attribute not set width: width attribute not set description: {\displaystyle l_{z}'=m_{l}\hbar \;,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a3f945c408d692391284a629617fe0b301776222 height: height attribute not set width: width attribute not set description: {\displaystyle m_{l}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a922b4921b214eaea71a73a22cdec40fa779b56 height: height attribute not set width: width attribute not set description: {\displaystyle m_{\ell }=-\ell ,(-\ell +1),\ldots ,(\ell -1),\ell \ \ } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fe2c14b5f5c18f417610a8c8203fb993aeac28e9 height: height attribute not set width: width attribute not set description: {\displaystyle \psi ^{*}\psi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc0f2f4718e07594442284bb1c9281ae73fa266d height: height attribute not set width: width attribute not set description: {\displaystyle \left|{\tfrac {1}{2}},{\tfrac {1}{2}}\right\rangle =e^{i\phi /2}\sin ^{\frac {1}{2}}\theta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/38d86a5895256289c6ff282461e4a708063cabcb height: height attribute not set width: width attribute not set description: {\displaystyle \left|{\tfrac {1}{2}},-{\tfrac {1}{2}}\right\rangle =e^{-i\phi /2}\sin ^{\frac {1}{2}}\theta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ad677029c4490e6999fdc855d699fb1524fff025 height: height attribute not set width: width attribute not set description: {\displaystyle l_{z}=q_{x}p_{y}-q_{y}p_{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3a6c68c8587292efa2fe70b67cdde43def6cbd43 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}q_{1}&={\frac {q_{x}+p_{y}}{\sqrt {2}}}&q_{2}&={\frac {q_{x}-p_{y}}{\sqrt {2}}}\\p_{1}&={\frac {p_{x}-q_{y}}{\sqrt {2}}}&p_{2}&={\frac {p_{x}+q_{y}}{\sqrt {2}}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/29cb5168f60f70f4678cf32583eb0cc71c9adbc2 height: height attribute not set width: width attribute not set description: {\displaystyle l_{z}={\tfrac {1}{2}}\left(p_{1}^{2}+q_{1}^{2}\right)-{\tfrac {1}{2}}\left(p_{2}^{2}+q_{2}^{2}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7681f5eba598d7964e06856356c7a5e152429bb8 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}h_{1}&={\tfrac {1}{2}}\left(p_{1}^{2}+q_{1}^{2}\right)\\h_{2}&={\tfrac {1}{2}}\left(p_{2}^{2}+q_{2}^{2}\right)\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4d9a872a55b209f2eb7cc23a71e5e1541bd1f4 height: height attribute not set width: width attribute not set description: {\displaystyle h_{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7fa4324515cc7343ee952e3840a1bb1aa8c7f74c height: height attribute not set width: width attribute not set description: {\displaystyle h_{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ebf9bf644e458dcbfbcb50d1c13520b7e50b6cf3 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}l^{2}\psi &=\hbar ^{2}\ell (\ell +1)\psi \\l_{z}\psi &=\hbar m\psi \\h_{1}\psi &=\hbar \left(n_{1}+{\tfrac {1}{2}}\right)\psi \\h_{2}\psi &=\hbar \left(n_{2}+{\tfrac {1}{2}}\right)\psi \end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e4c0513851e56ec97c37a3e9b89ab9256cfab135 height: height attribute not set width: width attribute not set description: {\displaystyle n_{1},n_{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3234c5338efac48cf9ed63ca62c89923d8ae2f40 height: height attribute not set width: width attribute not set description: {\displaystyle m=\left(n_{1}+{\tfrac {1}{2}}\right)-\left(n_{2}+{\tfrac {1}{2}}\right)=n_{1}-n_{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc height: height attribute not set width: width attribute not set description: {\displaystyle m} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/vector_model_of_orbital_angular_momentum.svg/250px-vector_model_of_orbital_angular_momentum.svg.png height: 285 width: 250 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/682399b5a2ae37a3b5b13a0e4e3f7348fa3c0ab4 height: height attribute not set width: width attribute not set description: {\displaystyle \ell =2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b474f9f14d68259a8639ddc40e1e0ffcacf10055 height: height attribute not set width: width attribute not set description: {\displaystyle m_{\ell }=-2,-1,0,1,2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5aa934176ab22fa7865613084429ff0d03c4aab1 height: height attribute not set width: width attribute not set description: {\displaystyle |l|={\sqrt {l^{2}}}=\hbar {\sqrt {6}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d6f84bd8aa27b634839e3ddbef7e0bae05db5bd1 height: height attribute not set width: width attribute not set description: {\displaystyle \hbar {\sqrt {6}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3ebc06e436594a115abefe1f78041e044bc4946f height: height attribute not set width: width attribute not set description: {\displaystyle l_{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/520bb78f6e5574034e2ef81bd1ba0b6d416537a9 height: height attribute not set width: width attribute not set description: {\displaystyle l_{y}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8 height: height attribute not set width: width attribute not set description: {\displaystyle l} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8e3574caae6e8c5d89aee459f68f93216dd22f6 height: height attribute not set width: width attribute not set description: {\displaystyle l_{z}/\hbar } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4a900c81527b0874a46027f0e7c9308a7a522766 height: height attribute not set width: width attribute not set description: {\displaystyle r({\hat {n}},\phi )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d125dccc556f5c8b0bf98a4f3847590b3f353bd4 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {n}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c4f45938f12d5ecd8f41f979cb819b552d701b45 height: height attribute not set width: width attribute not set description: {\displaystyle \phi \rightarrow 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/17326aeae4fa4c823e540d305e80cc0f7f708625 height: height attribute not set width: width attribute not set description: {\displaystyle j_{\hat {n}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7df6c24916e10da6f9e0eb908a8b70533c8bdca6 height: height attribute not set width: width attribute not set description: {\displaystyle j_{\hat {n}}\equiv i\hbar \lim _{\phi \rightarrow 0}{\frac {r\left({\hat {n}},\phi \right)-1}{\phi }}=\left.i\hbar {\frac {\partial r\left({\hat {n}},\phi \right)}{\partial \phi }}\right|_{\phi =0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d65d290ca91cd8a35f6ab8e698cb20d27366a3ad height: height attribute not set width: width attribute not set description: {\displaystyle r\left({\hat {n}},\phi _{1}+\phi _{2}\right)=r\left({\hat {n}},\phi _{1}\right)r\left({\hat {n}},\phi _{2}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4377c8bf313cfade761689c69589fd9f5cb9d1 height: height attribute not set width: width attribute not set description: {\displaystyle r\left({\hat {n}},\phi \right)=\exp \left(-{\frac {i\phi j_{\hat {n}}}{\hbar }}\right)} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/8/85/rotationoperators.svg/300px-rotationoperators.svg.png height: 222 width: 300 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8178f86be8df1997d76a57a46fbb4f2da99e820 height: height attribute not set width: width attribute not set description: {\displaystyle r_{\text{spatial}}\left({\hat {n}},\phi \right)=\exp \left(-{\frac {i\phi l_{\hat {n}}}{\hbar }}\right),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c93c39b2db565f568d238ef4e7c04b9da93e5d0d height: height attribute not set width: width attribute not set description: {\displaystyle r_{\text{internal}}\left({\hat {n}},\phi \right)=\exp \left(-{\frac {i\phi s_{\hat {n}}}{\hbar }}\right),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/630dad93a8a9cf6ba18758ebd7687c3c0652ecb7 height: height attribute not set width: width attribute not set description: {\displaystyle r\left({\hat {n}},\phi \right)=r_{\text{internal}}\left({\hat {n}},\phi \right)r_{\text{spatial}}\left({\hat {n}},\phi \right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fa348f3ab4a5447d384efd6056fde2f60bacfca6 height: height attribute not set width: width attribute not set description: {\displaystyle r\left({\hat {n}},360^{\circ }\right)=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/24fb8a038d374865698c21a1ff878feaef90a12e height: height attribute not set width: width attribute not set description: {\displaystyle r\left({\hat {n}},360^{\circ }\right)=-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7c5ab77575d890ca2ea9bd23989a803792dd2b98 height: height attribute not set width: width attribute not set description: {\displaystyle r\left({\hat {n}},360^{\circ }\right)=+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/00b821ca2fd053bacb0cb58a1eea9e6c5ac39e0f height: height attribute not set width: width attribute not set description: {\displaystyle r_{\text{spatial}}\left({\hat {n}},360^{\circ }\right)=+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f19872df77f4170b032e3a6ff6faac5d820df277 height: height attribute not set width: width attribute not set description: {\displaystyle r_{\text{spatial}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33 height: height attribute not set width: width attribute not set description: {\displaystyle r} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b554498f30385be41f19ac7326e1ee989acf89af height: height attribute not set width: width attribute not set description: {\displaystyle r_{\text{internal}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5bcfd7c61728801e6905d7c3c0071700b652a1bb height: height attribute not set width: width attribute not set description: {\displaystyle +1=r_{\text{spatial}}\left({\hat {z}},360^{\circ }\right)=\exp \left(-2\pi il_{z}/\hbar \right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/725f8f40d81dbb7feb82d20138a3b4f15265adcd height: height attribute not set width: width attribute not set description: {\displaystyle l_{z}|\psi \rangle =m\hbar |\psi \rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/41975c3c62c464863fde02647f8e728237b277f1 height: height attribute not set width: width attribute not set description: {\displaystyle e^{-2\pi im}=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c1c429af2a5f67ca03dabc80a872dfd9a3768b height: height attribute not set width: width attribute not set description: {\displaystyle |\psi _{0}\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d31a078f593d806c765984f72357ef6c6d93bd28 height: height attribute not set width: width attribute not set description: {\displaystyle r\left({\hat {n}},\phi \right)\left|\psi _{0}\right\rangle } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/369267d5eae15a7478ebb52c71fcec1449a10dc9 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathfrak {su}}(2)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fb4f1d3d3bf3da64b92af1a1018ce00545808b9d height: height attribute not set width: width attribute not set description: {\displaystyle {\mathfrak {so}}(3)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/53d244ab156038d6de05d04384ab3fcc72c2aeb2 height: height attribute not set width: width attribute not set description: {\displaystyle rhr^{-1}=h} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/55ca790f49501a692d19581c1e02757584a8a859 height: height attribute not set width: width attribute not set description: {\displaystyle [h,r]=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/316d3c62d119440ee1b4fd5bfbce4e40e6263a07 height: height attribute not set width: width attribute not set description: {\displaystyle [h,\mathbf {j} ]=\mathbf {0} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7e8cceeadf87ea574efdd71a4deeffa1191f0a06 height: height attribute not set width: width attribute not set description: {\displaystyle \left|\mathbf {r} \right|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fd9653f0f071aa78c550b57322444c4273127b76 height: height attribute not set width: width attribute not set description: {\displaystyle \left(j_{1}\right)_{z},\left(j_{1}\right)^{2},\left(j_{2}\right)_{z},\left(j_{2}\right)^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/75cd71af1ef180b00053a4dcc485778d84be96ac height: height attribute not set width: width attribute not set description: {\displaystyle \left(j_{1}\right)^{2},\left(j_{2}\right)^{2},j^{2},j_{z}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3eff329acb847dcbc08e46db7d68c92fa0a174ba height: height attribute not set width: width attribute not set description: {\displaystyle \left(j_{1}\right)^{2},\left(j_{2}\right)^{2},j^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/05026dea6b5f2f44e9083ccacacb5bacd55fce8d height: height attribute not set width: width attribute not set description: {\displaystyle j\in \left\{\left|j_{1}-j_{2}\right|,\left(\left|j_{1}-j_{2}\right|+1\right),\ldots ,\left(j_{1}+j_{2}\right)\right\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4ed9822e4fd44d5ce4ab2e7138ba47dc1ed6777b height: height attribute not set width: width attribute not set description: {\displaystyle l^{2},s^{2},j^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0361e1d9c1dc399df90dd9b4857c58af43a7316a height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\mathbf {l} &=i\hbar \left({\frac {\hat {\boldsymbol {\theta }}}{\sin(\theta )}}{\frac {\partial }{\partial \phi }}-{\hat {\boldsymbol {\phi }}}{\frac {\partial }{\partial \theta }}\right)\\&=i\hbar \left({\hat {\mathbf {x} }}\left(\sin(\phi ){\frac {\partial }{\partial \theta }}+\cot(\theta )\cos(\phi ){\frac {\partial }{\partial \phi }}\right)+{\hat {\mathbf {y} }}\left(-\cos(\phi ){\frac {\partial }{\partial \theta }}+\cot(\theta )\sin(\phi ){\frac {\partial }{\partial \phi }}\right)-{\hat {\mathbf {z} }}{\frac {\partial }{\partial \phi }}\right)\\l_{+}&=\hbar e^{i\phi }\left({\frac {\partial }{\partial \theta }}+i\cot(\theta ){\frac {\partial }{\partial \phi }}\right),\\l_{-}&=\hbar e^{-i\phi }\left(-{\frac {\partial }{\partial \theta }}+i\cot(\theta ){\frac {\partial }{\partial \phi }}\right),\\l^{2}&=-\hbar ^{2}\left({\frac {1}{\sin(\theta )}}{\frac {\partial }{\partial \theta }}\left(\sin(\theta ){\frac {\partial }{\partial \theta }}\right)+{\frac {1}{\sin ^{2}(\theta )}}{\frac {\partial ^{2}}{\partial \phi ^{2}}}\right),\\l_{z}&=-i\hbar {\frac {\partial }{\partial \phi }}.\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/27a9afb4a4c672db4b3b6e3ba04ed161be68e1dd height: height attribute not set width: width attribute not set description: {\displaystyle \delta ={\frac {1}{r^{2}}}{\frac {\partial }{\partial r}}\left(r^{2}\,{\frac {\partial }{\partial r}}\right)-{\frac {l^{2}}{\hbar ^{2}r^{2}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7abea16692bbdc30b47816eead60c8ffe77e52cf height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}l^{2}\left|\ell ,m\right\rangle &=\hbar ^{2}\ell (\ell +1)\left|\ell ,m\right\rangle \\l_{z}\left|\ell ,m\right\rangle &=\hbar m\left|\ell ,m\right\rangle \end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e108495bd0a8943c0f4b63f2f903b24eb7e3380a height: height attribute not set width: width attribute not set description: {\displaystyle \left\langle \theta ,\phi |\ell ,m\right\rangle =y_{\ell ,m}(\theta ,\phi )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4cfde86a3f7ec967af9955d0988592f0693d2b19 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a height: height attribute not set width: width attribute not set description: {\displaystyle \gamma } |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://en.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
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http://en.wikipedia.org/w/resources/assets/poweredby_mediawiki.svg height: 31 width: 88 description: powered by mediawiki |
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